Binding energy and diamagnetic susceptibility of donor impurities in quantum dots with different geometries and potentials

•Symmetry breaking of the step-like structure of the energy level in saw-tooth potential profiles.•Wave localization or delocalization in triangular, rectangular, saw-tooth & Sinusoidal Potentials.•Maximum (minimum) binding energy and diamagnetic susceptibility in the cylindrical (spherical) quantum dots determined.•We illustrates that spherical quantum dot systems is more tunable than the cylindrical ones.•The composition parameter x do not have a unique effect on systems with different geometries and confining potential shapes. We study the binding energy and diamagnetic susceptibility of a donor impurity in multi-well cylindrical and spherical quantum dot systems with triangular, rectangular, saw-tooth and sinusoidal-shaped confining potentials. To tune the binding energy and diamagnetic susceptibility of a donor impurity, we used different parameters such as number of wells, composition parameter x, shape on the potential profile, shape of the quantum dot, etc. We discuss the effect of the symmetry on the step-like structure of the energy level versus the number of wells. We describe the wave function engineering (localization or delocalization) in proposed systems. We determined the situations that lead to the maximum (minimum) binding energy and diamagnetic susceptibility in the cylindrical (spherical) quantum dots. By using the number of wells, we change the monotonic increasing behavior of binding energy to a monotonic decreasing behavior. We illustrate that spherical quantum dot systems are more tunable than the cylindrical ones.